Question

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

Answer 1

$the \: graph \: of \: y = 3 {x}^{2} + 7x + m \\ have \: two \: x \: intercepts \: if \: the \\ quadratic \: equation \: \\ 3 {x}^{2} + 7x + m = 0 \: has \: real \: and \: \\ distinct \: roots. \: so \\ {7}^{2} - 4 \times 3 \times m > 0 \\ m < \frac{49}{12}$